Polarization of Light Scattered by Solar System Bodies and the Aggregate Model of Dust Particles

The present study considers the dependence of characteristics of light scattering by aggregate particles on the refractive index, size, and number of spherical particles composing the aggregate, as well as on the structure and porosity of the cluster. The parameters were varied in sufficiently wide ranges to let a coherent picture of the polarimetric properties of relatively small aggregate particles emerge (the size parameter of the aggregate is less than 10). It was shown that, in the framework of the aggregate model, the behavior of polarization phase curves observed for both comets and regolith surfaces can be explained. The modeling carried out confirms that the sizes of the cometary dust particles are larger than the wavelength. However, the grains forming the cometary dust particles or the regolith (or details of the particle surface) have a size less than 0.3–0.5 m. This agrees with estimates obtained by other methods. The determining role in the formation of the polarization phase curve is played by the structure of the external layer of the clusters. The appearance of the negative branch of polarization and its shape substantially depend on the effectiveness of the interference of multiply scattered waves and on the interaction in the near field at these phase angles. Interference and interaction in the near field in turn are determined by the sizes of elementary scatterers and the structure of the ensemble. If the number of constituent particles in the aggregate is larger than several tens, its role in the formation of the negative branch of polarization is minor, while the influence on the polarization maximum position is rather substantial. The polarimetric data alone cannot provide a unique estimate of the refractive index: the brightness measurements must be invoked as well. For a more complete quantitative interpretation of the observations, the scattering matrix of aggregates comparable in size to or larger than the wavelength must be calculated in the short- and long-wavelength ranges, which still encounters serious theoretical and technical difficulties. Moreover, in order to obtain unique results, it is obvious that the spectral range of observations must be extended and that other types of measurements, such as spectroscopic ones, must also be used.     

Light Scattering by Aggregate Particles Comparable in Size to Wavelength: Application to Cometary Dust

Many naturally occurring particles (including, most likely, cometary dust) have an aggregate structure. We study the scattering properties of polydisperse independent aggregate particles (clusters) comparable in size to visible wavelengths. The sizes of the monomers constituting a cluster play a significant role in forming the angular dependences of intensity and linear polarization of the scattered light. Irregularly structured aggregates composed of a moderate number of spheres (<50) with size parameters 1.3–1.65 exhibit properties typical of cometary dust particles: a slight increase in backscattering intensity, a negative polarization at small phase angles, an inversion phase angle close to the observed one, an increase in brightness, and a linear polarization with increasing wavelength. In this case, the imaginary part of the refractive index for particles can increase with decreasing wavelength in the visible spectral range, which is typical of silicates with an admixture of iron or organic material. The spectral dependence of extinction efficiency for aggregates is less steep than that for equivalent spherical particles, and its maximum is shifted to larger size parameters. Therefore, when analyzing extinction measurements, the scatterer shape must be taken into account to avoid underestimation of the scattering-particle sizes.     

Scattering of Light by Composite Particles in a Planetary Surface

It has been proposed that composite particles containing internal scatterers may provide the explanation for the fact that most photometric studies of planetary surfaces based on Hapke's model of bidirectional reflectance have found the planetary particles to exhibit moderately backscattering phase functions. However, an implicit assumption made in this explanation is that the scattering by composite particles containing multiple internal inclusions in a planetary surface can still be adequately computed using standard radiative transfer theory assuming the composite particles to be the fundamental individual scatterers even though such particles are necessarily in close proximity to each other. In this paper, this assumption is explored by examining the effects of close packing on the light scattering by spherical particles containing isotropic internal scatterers using a Monte Carlo routine. As expected, classical radiative transfer (assuming a random distribution of scattering particles) coupled with the assumption that the composite particle is the fundamental scatterer provides a good approximation in the high porosity limit. However, even for porosities as high as 90% the effects of close packing are clearly seen with the radiative transfer calculation underestimating the scattering by ∼10% at high incidence, emission, and phase angles. As the porosity is lowered further, the discrepancy becomes more severe and can reach 50% or more. In contrast, assuming the individual scatterer properties in the radiative transfer calculation leads to a substantial overestimate of the scattering even for porosities as low as 27.5%. This suggests that parameters derived using the classical radiative transfer theory will yield results intermediate between those of the composite as a whole and those of the internal scatterers. Thus, one should exercise caution in interpreting the results of models based on classical radiative transfer theory in terms of the physical properties of the surface particles and, where possible, the bidirectional reflectance of densely packed composite particles should be computed using more accurate methods such as the stochastic radiative transfer theory.     

Polarization of Light Scattered by Fluffy Particles (PROGRA Experiment)

This work was carried out with the PROGRA² experiment developed to measure the angular dependence of the polarization of light scattered by dust particles. The dust samples are fluffy aggregates (size range 0.01-1 mm) with constituent grains of about 10 nm. Various setups were used: samples deposited on surfaces, the same samples lifted under the effect of a draft, and particles levitating in microgravity conditions on board the CNES dedicated aircraft. For deposited particles, the maximum value of polarization (P_max) follows the Umov law. For a cloud of particles (P_max) near 100° phase angle decreases when: (i) multiple scattering between the particles—or between the grains inside the particles—increases, or (ii) the real part of the refractive index of the materials increases, or (iii) the size parameter of the constituent grains increases between 0.05 and 0.5. A negative branch in the polarization phase curve is found for deposited samples. For levitating particles made of a single material and a single size distribution, a positive increase of polarization appears at phase angles smaller than 20°; for mixtures of these materials the polarization is negative at the same phase angles. These results are compared to modeling results as well as to polarimetric observations of comets.     

Opposition Effects in Brightness,Color, and Polarization of Comet 1P/Halley: Comparison with Atmosphereless Solar System Bodies

Systematic and uniform sets of photometric and polarimetric observations of comet 1P/Halley have been analyzed. The phase dependence of brightness for comet Halley was obtained at phase angles α ranging from 1.4° ≤ α ≤ 65°. The following parameters were determined: the amplitude of the opposition effect Δm = 0.75^m ± 0.06^m; the half-width at a half-maximum of intensity HWHM = 6.4° ± 1.6°; the linear phase coefficient β = 0.0045 ± 0.0001 mag/deg for α from 30° ≤ α ≤ 65°; and the phase angle at which a nonlinear increase in brightness starts, α _opp ≈ 31°. For the first time, the phase-angle dependence was obtained for the color of the dust of comet Halley: the color index BC-RC systematically decreases with increasing phase angle. Such a phase behavior of the dust color can be caused by the decrease in the mean size of dust particles that occurs when the comet approaches the Sun. For comet Halley, the negative polarization branch is almost symmetric; the minimal value of polarization is P _min = −1.54% at a phase angle α_min = 10.5°, and the inversion angle is α_inv = 21.7°. A comparative analysis of the phase functions of brightness and polarization has been performed for the cometary dust and atmosphereless bodies. Among the latter are low-albedo asteroids of the P and C types (102 Miriam and 47 Aglaja, respectively), as well as Deimos; high-albedo objects, such as the E-type asteroid 64 Angelina and the icy satellite of Jupiter Europa; and the Moon with its intermediate albedo. The possibility of a weak depression in the negative polarization branch of comets Halley and 47P/Ashbrook-Jackson at phase angles smaller than 2° is discussed.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 4, 2005, pp. 353–363.Original Russian Text Copyright © 2005 by Rosenbush.     

Characteristics of Light Scattering at Small Phase Angles by Surfaces Consisting of Spherical Particles

We present the results of measurements of the phase dependences of brightness and of the polarization and depolarization characteristics for surfaces consisting of spherical glass particles in the phase-angle range from 0.1° to 5.0°. The measurements are performed using the laboratory photometer/polarimeter of Kharkov Astronomical Observatory and the photometer of Jet Propulsion Laboratory. An optically thick layer of transparent-glass spheres with mean size of about 57 m and refractive index of 1.44 exhibits a strong opposition effect due to single scattering. The contribution of interparticle scattering is nearly independent of the phase angle. At an angle of 0.4°, the spheres exhibit a glory ring that manifests itself in the phase behavior of all characteristics investigated. Small details are seen on the curves when a monochromatic radiation source is used for measurements. Their occurrence is confirmed by calculations based on the Mie theory. The unusual behavior of the phase dependences of reflectivity, degree of polarization, and color index for layers composed of spherical particles can be used to search for sites of possible deposits of spherical glass (or ice) particles in regoliths of atmosphereless celestial bodies.     

Light Curves of Selected Comets: Photometric Parameters and Flares

The light curves of four comets were constructed and analyzed. The photometric parameters H _yand nwere determined. The derived values of H _yand nwere compared with those obtained by other authors. The parameter nfor Comet Ikeya–Secchi was found to vary. A list of flares in these comets was compiled.     

Evaluation of Light Flashes Caused by Impacts of Small Comets on the Surface of the Moon

Images of the dayglow of the Earth's atmosphere in the ultraviolet wavelength region obtained by the photometer of the spacecraft Dynamics Explorer revealed dark spots of the order of 50 km in diameter. These atmospheric holes were interpreted by the American physicist Frank as concentrations of water vapor formed as a result of the disintegration and vaporization of so-called small comets at high altitudes. An analysis of the same images showed that their explanation requires a frequency of comet collisions with the Earth as high as 20 events a minute! This sensational hypothesis evoked a heated scientific debate. The paper below contains an analysis of the possibility of observing Frank's hypothetical comets during their collisions with the Moon. By solving a two-dimensional radiative–gasdynamic problem, the authors demonstrate that the flashes occurring during such impacts can be observed from the Earth with ordinary telescopes.     

根据数字化巡天光盘测定天体E或V星等

用目视和底片密度扫描的办法从帕洛玛巡天底片得到天体星等资料已有许多作者讨论过，其结果得到广泛的应用．考虑到帕洛玛底片已经数字化并做出了数字化巡天光盘（ＤＳＳ），若从它直接得到测光资料将更为方便，为此，我们发展了直接从ＤＳＳ中得到北天天区天体（δ３°）Ｅ或Ｖ星等的软件，其测量Ｅ星等的精度为０．３７ｍ（１３．５ｍＥ１８．０ｍ），Ｖ星等的精度为０．４２ｍ（１４．４ｍＶ１８．９ｍ）．     

On Errors in Constructing the Polarization Phase Dependences for Solar System Bodies

In astrophysical studies of Solar System bodies, the measured values of the linear polarization degree P_obs and the position angle of the polarization plane θ are usually considered relative to the plane orthogonal to the scattering plane; and the resulting quantities are designated as P_r and θ_r, respectively. Parameters of the phase curve of polarization P_r = f(α) serve for determining the physical characteristics of grains composing the regolith surfaces of such bodies as, for example, the Moon, Mercury, asteroids, and planetary satellites, or the polydisperse media, such as cometary comae and tails. In this paper it has been shown that the error in the polarization degree grows \({\sigma _{{P_r}}}\) due to the error \({\sigma _{{\theta _{obs}}}}\) in determining the position angle. The interrelations between these errors were obtained, and the conditions, under which the values of the linear polarization degree P_r relative to the orthogonal system can be used to analyze the phase dependences of polarization, were formulated.     

Seyfert 2 星系光谱偏振的汤姆逊散射机制

利用简单的ｔｏｒｎｓ束流模型定量计算Ｓｅｙｆｅｒｔ２型星系的偏振度和散射流量的角分布,在“一次电子散射”的假定下,得到偏振度约为１０％～８０％．而偏振流量的角分布与ｔｏｒｎｓ半张角θｃ和观测角φｏ都有关．特别是当φｏ　５５°时,观测方向的流量和总的散射流量的比值为一定值（０．１６）．用这种纯电子散射模型来解释ＮＧＣ１０６８的光谱偏振更为合适．对于其它一些具有低的偏振度的Ｓｅｙｆｅｒｔ２星系,尘埃的作用则不能忽略．     

The Opposition Effect and Negative Polarization of Structural Analogs for Planetary Regoliths

To better understand the negative polarization and brightness opposition effects observed on airless celestial bodies, we carried out simultaneous photometric and polarimetric measurements of laboratory samples that simulate the structure of planetary regoliths. Computer modeling of shadow-hiding and coherent backscatter in regolith-like media are also presented. The laboratory investigations were carried out with a photometer/polarimeter at phase angles covering 0.2°-4° and wavelengths of 0.63 and 0.45 μm. We studied samples that characterize a variety of microscopic structures and albedos. A particle-size dependence of the negative branch of polarization for powdered dielectric surfaces was found. Colored samples such as a powder Fe₂O₃ exhibit a very prominent wavelength dependence of the photometric and polarimetric opposition phenomena. Metallic powders usually exhibit a wide branch of the negative polarization independent of the size of particles. For fine dielectric powders, both opposition phenomena become more prominent when the samples were compressed. Our computer modeling based on ray tracing in particulate media shows that shadow-hiding affects the negative polarization only in combination with the coherent backscatter enhancement. Modeling reveals that scattering orders higher than second contribute to negative polarization even in dark particulate surfaces. Our model qualitatively reproduces the effects of varying sample-compression that we observed in the laboratory. Our experimental and computer modeling studies mutually confirm that the degree of polarization for highly reflective dielectric surfaces depends not only on phase angle but also on surface tilt. Even at exactly zero phase the degree of polarization for tilted surfaces can be nonzero. A tilt of the surface normal to the scattering plane gives a parallel shift of the negative polarization branch to large values of |P|. The tilt in the perpendicular plane gives the same shift in the direction of positive polarization. At exactly zero phase angle, a celestial body of irregular shape can exhibit nonzero polarization even in integral polarimetric observations.     

Effects of the Triaxiality on the Rotation of Celestial Bodies: Application to the Earth,Mars and Eros

In this paper we discuss the influence of the triaxiality of a celestialbody on its free rotation, i.e. in absence of any external gravitationalperturbation. We compare the results obtained through two different analytical formalisms, one established from Andoyer variables by usingHamiltonian theory, the other one from Euler's variables by usingLagrangian equations. We also give a very accurate formulation of thepolar motion (polhody) in the case of a small amplitude of this motion.Then, we carry out a numerical integration of the problem, with aRunge–Kutta–Felberg algorithm, and for the two kinds of methods above, that we apply to three different celestial bodies considered as rigid : the Earth, Mars, and Eros. The reason of this choice is that each of this body corresponds to a more or less triaxial shape.In the case of the Earth and Mars we show the good agreement betweenanalytical and numerical determinations of the polar motion, and theamplitude of the effect related to the triaxial shape of the body, whichis far from being negligible, with some influence on the polhody of theorder of 10 cm for the Earth, and 1 m for Mars. In the case of Eros, weuse recent output data given by the NEAR probe, to determine in detailthe nature of its free rotational motion, characterized by the presence ofimportant oscillations for the Euler angles due to the particularly largetriaxial shape of the asteroid.     

A Model for the Common Origin of Jupiter Family and Halley Type Comets

A numerical simulation of the Oort cloud is used to explain the observed orbital distributions and numbers of Jupiter-family (JF) and Halley-type (HT) short-period (SP) comets. Comets are given initial orbits with perihelion distances between 5 and 36 au, and evolve under planetary, stellar and Galactic perturbations for 4.5 Gyr. This process leads to the formation of an Oort cloud (which we define as the region of semimajor axes a > 1,000 au), and to a flux of cometary bodies from the Oort cloud returning to the planetary region at the present epoch. The results are consistent with the dynamical characteristics of SP comets and other observed cometary populations: the near-parabolic flux, Centaurs, and high-eccentricity trans-Neptunian objects. To achieve this consistency with observations, the model requires that the number of comets versus initial perihelion distance is concentrated towards the outer planetary region. Moreover, the mean physical lifetime of observable comets in the inner planetary region (q < 2.5 au) at the present epoch should be an increasing function of the comets’ initial perihelion distances. Virtually all observed HT comets and nearly half of observed JF comets come from the Oort cloud, and initially (4.5 Gyr ago) from orbits concentrated near the outer planetary region. Comets that have been in the Oort cloud also return to the Centaur (5 < q < 28 au, a < 1,000 au) and near-Neptune high-eccentricity regions. Such objects with perihelia near Neptune are hard to discover, but Centaurs with characteristics predicted by the model (e.g. large semimajor axes, above 60 au, or high inclinations, above 40°) are increasingly being found by observers. The model provides a unified picture for the origin of JF and HT comets. It predicts that the mean physical lifetime of all comets in the region q < 1.5 au is less than ～200 revolutions.     

Comets and the formation of planets

A morphological study of the physical and dynamical processes of planet formation is presented, with emphasis on the intermediary role of comet nuclei. Although guided by a particular model of the evolution of the pre-planetary solar nebula, implying the freezing-out of hydrogen in the region of the giant planets, the derivations and conclusions are of wider import, applicable to other cosmogonic models as well as to certain phases of star formation. The items evaluated physically, dynamically, or statistically comprise: (1) the total number mass of comets in Oort's cloud; (2) a re-evaluation of the diameters and masses of cometary nuclei; (3) the processes of nucleation from gravitational and Boltzmann instabilities of gaseous media to agglomerations of particulate matter as conditioned by inbuilt angular momentum; (4) the statistical-dynamical conditions and time scales of orbital interaction of comets with the planets and the consequences of disintegration.A consistent model proposes the formation of comets and planets in pre-planetary rings of the residual solar nebula, with subsequent ejection, chiefly by Jupiter, of the comets to Oort's sphere. Screening by absorbing matter is not only probable, but necessary to protect the comets from dis-integration during the process of ejection.Paper dedicated to Prof. H. C. Urey on the occasion of his 80th birthday on 29 April, 1973.This work has been currently supported by grants from the National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland.     

Search for New Parent Bodies of Meteoroid Streams Among Comets. I. Showers of Comets 126P/1996 P1 and 161P/2004 V2 with Radiants on Southern Sky

We deal with theoretical meteoroid streams the parent bodies of which are two Halley-type comets in orbits situated at a relatively large distance from the orbit of Earth: 126P/1996 P1 and 161P/2004 V2. For two perihelion passages of each comet in the far past, we model the theoretical stream and follow its dynamical evolution until the present. We predict the characteristics of potential meteor showers according to the dynamical properties of theoretical particles currently approaching the orbit of the Earth. Our dynamical study reveals that the comet 161P/2004 V2 could have an associated Earth-observable meteor shower, although no significant number of theoretical particles are identified with real, photographic, video, or radar meteors. However, the mean radiant of the shower is predicted on the southern sky (its declination is about −23°) where a relatively low number of real meteors has been detected and, therefore, recorded in the databases used. The shower of 161P has a compact radiant area and a relatively large geocentric velocity of ∼53 km s⁻¹. A significant fraction of particles assumed to be released from comet 126P also cross the Earth’s orbit and, eventually, could be observed as meteors. However, their radiant area is largely dispersed (declination of radiants spans from about +60° to the south pole) and, therefore, mixed with the sporadic meteor background. An identification with real meteors is practically impossible.     

The Processing and Classification for the Spectra of Six Comets

In order to explore the relationship between comets and asteroids, the spectra of six comets, including 78P, C/2009 P1, 49P, C/2010 G2, C/2010 S1, and C/2011 F1, have been observed with the 2.16 m telescope at the Xinglong Observing Station of National Astronomical Observatories. At the same time, the spectra of some sun-like stars are also observed. The IRAF (Image Reduction and Analysis Facility) software is used to process the obtained spectra, and to obtain the relative re?ectance spectra of the six comets. Then, they are compared with the 24 asteroid spectral types of the Bus-DeMeo taxonomy to derive the spectral distances of these comets. According to the order of the calculated spectral distances, the details of the re?ectance spectra, as well as the results of the K-S test, the asteroid spectral types which are most close to the spectra of these comets are ?nally determined.     

Directional Distribution of Observable Comets Induced by A Star Passage Through the Oort Cloud

We simulated the passage of a star through the Oort cometary cloud andanalyzed the resulting sample of observable long period comets, noting strong asymmetries in the directional distribution of the perihelion points of thosecomets. We discuss the results previously published byWeissman (1996) for the same case. An explanation is suggestedwhy the isotropic output can be obtained only for a very peculiar case. The``cometary shower' density variation with time is also presented and thetime-dependence of the directional distribution is discussed.     

应用商用CCD配备录像机进行天体定位的试验

本工作是为今后在1.2米望远镜上利用商用CCD配备录像机进行人卫快速精密定位观测所做的初步试验,其目的是在实验室里模拟检测商用CCD配备录像机后对星像的绝对及相对定位精度。通过使用不同图像板及录像带在不同幅度的CCD视频信号情况下的分组试验,得到了满足人卫观测的结果,CCD对绝对位置及相对位置的定位误差均小于±0.5个象元。本文还对误差产生的原因进行了初步分析。     

Regularization of Equations of Motion of Celestial Bodies. 2. Correction of the KS-Coordinate System in Numerical Integration

The idea of using various L-matrices in numerical integration of the regular equations, which describe the motion of small bodies of the Solar System, is developed. The problem of the optimal position of the radius vector and velocity at numerical integration in the KS-coordinate system is posed. The solution of this problem, which reduces the number of calculations of the vector of perturbing accelerations, is given. The transformation providing this optimal solution is suggested, and the results of numerical integration are given.